Answer: C) 4
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Plug in x = 0
f(x) = 2x^2 + 5
f(0) = 2(0)^2 + 5
f(0) = 5
Plug in x = 2
f(x) = 2x^2 + 5
f(2) = 2(2)^2 + 5
f(2) = 13
Now use the formula below to find the average rate of change (AROC) from x = a to x = b
AROC = ( f(b) - f(a) )/( b-a )
AROC = ( f(2) - f(0) )/( 2-0 )
AROC = ( 13 - 5 )/( 2 - 0)
AROC = 8/2
AROC = 4
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This is the same as finding the slope of the line through (0,5) and (2,13)
m = (y2 - y1)/(x2 - x1)
m = (13-5)/(2-0)
m = 8/2
m = 4